Calculate the amount of energy required to change the temperature of silica material from 350K to 450K. The enthalpy change associated with the temperature change from to in the constant pressure process is calculated as

Calculate the amount of energy required to change the temperature of silica material from 350K to 450K. The enthalpy change associated with the temperature change from 1 to T, in the constant pressure process is calculated as = EL"c,()dt (1) where C,(T) is the heat capacity as a function of temperature at constant pressure in J .kg . K-1 The heat capacity of a material as a function of temperature is frequently given in the form of polynomial relationships such as C,(T)=C(T)+A (T-T, j)+B (T3-T76), (2) where T and Tre are the measured temperatures and reference temperature in Kelvin. J C, kg. K Ckg. K .K 3. Fit Eq. (2) to the measured heat capacities using the linear least square method: 3.1 Use polyfit function from numpy library to calculate the coefficients C,(T) in J .kg . K". A in Jkg 1. K-? and B in Jkg 1.K- by least squares polynomial fit of the following data: T[K] J 7[K] T[K] J C. Lkg. 313.59 1045.04 382.85 1333.53 422.43 1629.69 333.38 1112.58 392.75 1399.71 432.34, 1727.41 353.15 1163.06 402.65 1465.91 442.21 1836.38 372.95 1277.84 412.54 1560.48 452.10 1939.65 Assume Ter=392.75 K. 3.2 Write the python program to calculate the coefficient of determination R' for Eq. (2). 3.3 Plot the experimental data as points and the fitted data by Eq. (2) as a line in the graph Co=f(T). 4. Calculate the amount of energy required to change the temperature of zeolite H-beta-38 material from 350K to 450K by 4.1 analytical integration of fitted polynomial by Eq. (2): 4.2 numerical integration using fitted polynomial by Eq.(2) - single application of trapezoidal rule; 4.3 numerical integration using fitted polynomial by Eq.(2) - multiple applications of trapezoidal rule with 2 and 4 sections; 4.4 numerical integration using fitted polynomial by Eq.(2) - single application of Simpson's 1/3; (2.2) - (2.4). Report h in K, AH in 1 kg and the true relative error e, in %. -1 Round numbers to five significant digits